Properties

Label 3234.2.x
Level 3234
Weight 2
Character orbit x
Rep. character \(\chi_{3234}(491,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 656
Sturm bound 1344

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Defining parameters

Level: \( N \) \(=\) \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3234.x (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3234, [\chi])\).

Total New Old
Modular forms 2816 656 2160
Cusp forms 2560 656 1904
Eisenstein series 256 0 256

Trace form

\( 656q + 4q^{3} - 164q^{4} - 5q^{6} + 8q^{9} + O(q^{10}) \) \( 656q + 4q^{3} - 164q^{4} - 5q^{6} + 8q^{9} - 6q^{12} + 12q^{15} - 164q^{16} - 5q^{18} - 30q^{19} + 5q^{24} + 180q^{25} - 26q^{27} + 30q^{30} + 38q^{31} - 47q^{33} - 12q^{34} - 7q^{36} + 36q^{37} + 50q^{39} - 10q^{40} - 8q^{45} - 20q^{46} + 4q^{48} + 25q^{51} - 20q^{52} - 4q^{55} - 45q^{57} + 30q^{58} - 8q^{60} + 60q^{61} - 164q^{64} + 20q^{66} - 68q^{67} + 42q^{69} + 20q^{72} + 30q^{73} + 23q^{75} + 80q^{78} + 20q^{79} + 20q^{81} + 14q^{82} - 60q^{85} + 90q^{90} + 42q^{93} - 80q^{94} - 14q^{97} - 146q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3234, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3234, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1617, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database